Euro zone officials examined three broad options for securing the private sector's involvement in a second bailout package for Greece during a teleconference last week, a document obtained by Reuters showed.

The document, an options paper dated July 16, is part of the euro zone's urgent efforts to secure sufficient financing for Athens for the next three years and put and end to market concern about the sustainability of debt in other euro zone countries, like Italy and Spain.

Euro zone leaders will discuss the second Greek bailout on Thursday.

The options outlined in the paper in a tabular form examine the interplay of various factors in the second financing package for Greece, depending on the type of private sector involvement.

The factors include impact on Greek credit ratings, how much money would be required from the euro zone's EFSF bailout fund, whether it would entail lower interest rates on EFSF loans and their extended maturity and Greek debt sustainability.

The first option was a buy-back of Greek debt and public sector credit enhancement. It would likely cause a downgrade of Greek debt to selective default or default by ratings agencies.

The paper did not spell out what form of credit enhancement, which is a way to improve creditworthiness, was under consideration.

Often-used forms of credit enhancement include securitization, collateral or other insurance that the lender will be paid back. Euro zone sources have said that under one of the scenarios being considered, new, 30-year Greek bonds that would replace existing debt in a swap operation could be backed by AAA paper, for example from the EFSF.

The paper did not provide any numbers, but said the cost to the euro zone bailout fund of the first option would be the cost of the new Greek program, plus the cost of the credit enhancements, the cost of a debt buy-back, the recapitalization of Greek banks and European Central Bank collateral, less the contribution from the private sector.

It would not require much lower EFSF interest rates or longer maturities. The impact on Greek debt sustainability of this option would depend on the interest rate and possible haircut in the private sector and the amount and discount in the debt buyback, the paper said.

The second option could be based on French banks' proposal for a debt rollover, which does not involve public sector credit enhancement. It would likely trigger a downgrade to selective default, the paper said.

The cost to the EFSF would be the cost of the new Greek program, plus the cost of recapitalizing Greek banks and ECB collateral, less the private sector contribution, the paper said.

The second option would also require lower lending rates from the EFSF and longer maturities on EFSF loans and the impact on Greek debt sustainability would depend on how low the EFSF rates are and how long the loan maturities are.

The third option could be based on a tax imposed on the financial sector, or a decentralized Vienna-type agreement with private banks, especially Greek ones which have large holdings of Greek debt, to maintain exposure. This option was unlikely to result in a selective default rating, the paper said.

The cost to the euro zone would be the smallest of the three options, as it would only comprise the cost of the new Greek financing program less the contribution from the private sector, the paper said.

It would still require lower EFSF lending rates and longer loan maturities, as they would determine the impact on Greek debt sustainability.

(Writing by Jan Strupczewski, editing by Rex Merrifield)